Question: Simplify the following expression: $x = \dfrac{-6k^2 + 6k + 252}{k - 7} $
First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-6$ , so we can rewrite the expression: $ x =\dfrac{-6(k^2 - 1k - 42)}{k - 7} $ Then we factor the remaining polynomial: $k^2 {-1}k {-42} $ ${-7} + {6} = {-1}$ ${-7} \times {6} = {-42}$ $ (k {-7}) (k + {6}) $ This gives us a factored expression: $\dfrac{-6(k {-7}) (k + {6})}{k - 7}$ We can divide the numerator and denominator by $(k + 7)$ on condition that $k \neq 7$ Therefore $x = -6(k + 6); k \neq 7$